Open Access

Weak convergence of an iterative sequence for accretive operators in Banach spaces

Fixed Point Theory and Applications20062006:35390

DOI: 10.1155/FPTA/2006/35390

Received: 21 November 2005

Accepted: 6 December 2005

Published: 8 June 2006


Let be a nonempty closed convex subset of a smooth Banach space and let be an accretive operator of into . We first introduce the problem of finding a point such that where is the duality mapping of . Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol'shteĭn and Tret'yakov in the Euclidean space to a Banach space. And using our theorem, we consider the problem of finding a fixed point of a strictly pseudocontractive mapping in a Banach space and so on.


Authors’ Affiliations

Department of Economics, Chiba University
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology


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© Koji Aoyama et al. 2006

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